Solve for $k$, $ -\dfrac{2}{12k - 4} = -\dfrac{k - 5}{6k - 2} + \dfrac{9}{3k - 1} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $12k - 4$ $6k - 2$ and $3k - 1$ The common denominator is $12k - 4$ The denominator of the first term is already $12k - 4$ , so we don't need to change it. To get $12k - 4$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ -\dfrac{k - 5}{6k - 2} \times \dfrac{2}{2} = -\dfrac{2k - 10}{12k - 4} $ To get $12k - 4$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ \dfrac{9}{3k - 1} \times \dfrac{4}{4} = \dfrac{36}{12k - 4} $ This give us: $ -\dfrac{2}{12k - 4} = -\dfrac{2k - 10}{12k - 4} + \dfrac{36}{12k - 4} $ If we multiply both sides of the equation by $12k - 4$ , we get: $ -2 = -2k + 10 + 36$ $ -2 = -2k + 46$ $ -48 = -2k $ $ k = 24$